实验四 决策树算法及应用

一：作业信息

博客班级	https://edu.cnblogs.com/campus/ahgc/AHPU-se-JSJ18
作业要求	https://edu.cnblogs.com/campus/ahgc/machinelearning/homework/12086
作业目标	决策树算法及应用
学号	3180701325
【实验目的】

理解决策树算法原理，掌握决策树算法框架；
理解决策树学习算法的特征选择、树的生成和树的剪枝；
能根据不同的数据类型，选择不同的决策树算法；
针对特定应用场景及数据，能应用决策树算法解决实际问题。
【实验内容】

设计算法实现熵、经验条件熵、信息增益等方法。
实现ID3算法。
熟悉sklearn库中的决策树算法；
针对iris数据集，应用sklearn的决策树算法进行类别预测。
针对iris数据集，利用自编决策树算法进行类别预测。
【实验报告要求】

对照实验内容，撰写实验过程、算法及测试结果；
代码规范化：命名规则、注释；
分析核心算法的复杂度；
查阅文献，讨论ID3、5算法的应用场景；
【实验过程】

In[1]：

import numpy as np
import pandas as pd
import matplotlib.pyplot as plt
%matplotlib inline
from sklearn.datasets import load_iris
from sklearn.model_selection import train_test_split
from collections import Counter
import math
from math import log
import pprint
In[2]：

def create_data():
datasets = [['青年', '否', '否', '一般', '否'],
['青年', '否', '否', '好', '否'],
['青年', '是', '否', '好', '是'],
['青年', '是', '是', '一般', '是'],
['青年', '否', '否', '一般', '否'],
['中年', '否', '否', '一般', '否'],
['中年', '否', '否', '好', '否'],
['中年', '是', '是', '好', '是'],
['中年', '否', '是', '非常好', '是'],
['中年', '否', '是', '非常好', '是'],
['老年', '否', '是', '非常好', '是'],
['老年', '否', '是', '好', '是'],
['老年', '是', '否', '好', '是'],
['老年', '是', '否', '非常好', '是'],
['老年', '否', '否', '一般', '否'],
]
labels = [u'年龄', u'有工作', u'有自己的房子', u'信贷情况', u'类别']
# 返回数据集和每个维度的名称
return datasets, labels
In[3]：

datasets, labels = create_data()
In[4]：

train_data = pd.DataFrame(datasets, columns=labels)
In[5]：

train_data
Out[5]：

In[6]：

熵

def calc_ent(datasets):
data_length = len(datasets)
label_count = {}
for i in range(data_length):
label = datasets[i][-1]
if label not in label_count:
label_count[label] = 0
label_count[label] += 1
ent = -sum([(p / data_length) * log(p / data_length, 2)
for p in label_count.values()])
return ent

def entropy(y):

"""

Entropy of a label sequence

"""

hist = np.bincount(y)

ps = hist / np.sum(hist)

return -np.sum([p * np.log2(p) for p in ps if p > 0])

经验条件熵

def cond_ent(datasets, axis=0):
data_length = len(datasets)
feature_sets = {}
for i in range(data_length):
feature = datasets[i][axis]
if feature not in feature_sets:
feature_sets[feature] = []
feature_sets[feature].append(datasets[i])
cond_ent = sum(
[(len(p) / data_length) * calc_ent(p) for p in feature_sets.values()])
return cond_ent

信息增益

def info_gain(ent, cond_ent):
return ent - cond_ent

def info_gain_train(datasets):
count = len(datasets[0]) - 1
ent = calc_ent(datasets)
# ent = entropy(datasets)
best_feature = []
for c in range(count):
c_info_gain = info_gain(ent, cond_ent(datasets, axis=c))
best_feature.append((c, c_info_gain))
print('特征({}) - info_gain - {:.3f}'.format(labels[c], c_info_gain))
# 比较大小
best_ = max(best_feature, key=lambda x: x[-1])
return '特征({})的信息增益最大，选择为根节点特征'.format(labels[best_[0]])
In[7]：

info_gain_train(np.array(datasets))
Out[7]：

In[8]：

定义节点类 二叉树

class Node:
def init(self, root=True, label=None, feature_name=None, feature=None):
self.root = root
self.label = label
self.feature_name = feature_name
self.feature = feature
self.tree = {}
self.result = {
'label:': self.label,
'feature': self.feature,
'tree': self.tree
}

def __repr__(self):
    return '{}'.format(self.result)

def add_node(self, val, node):
    self.tree[val] = node

def predict(self, features):
    if self.root is True:
        return self.label
    return self.tree[features[self.feature]].predict(features)

class DTree:
def init(self, epsilon=0.1):
self.epsilon = epsilon
self._tree = {}

# 熵
@staticmethod
def calc_ent(datasets):
    data_length = len(datasets)
    label_count = {}
    for i in range(data_length):
        label = datasets[i][-1]
        if label not in label_count:
            label_count[label] = 0
        label_count[label] += 1
    ent = -sum([(p / data_length) * log(p / data_length, 2)
                for p in label_count.values()])
    return ent

# 经验条件熵
def cond_ent(self, datasets, axis=0):
    data_length = len(datasets)
    feature_sets = {}
    for i in range(data_length):
        feature = datasets[i][axis]
        if feature not in feature_sets:
            feature_sets[feature] = []
        feature_sets[feature].append(datasets[i])
    cond_ent = sum([(len(p) / data_length) * self.calc_ent(p)
                    for p in feature_sets.values()])
    return cond_ent

# 信息增益
@staticmethod
def info_gain(ent, cond_ent):
    return ent - cond_ent

def info_gain_train(self, datasets):
    count = len(datasets[0]) - 1
    ent = self.calc_ent(datasets)
    best_feature = []
    for c in range(count):
        c_info_gain = self.info_gain(ent, self.cond_ent(datasets, axis=c))
        best_feature.append((c, c_info_gain))
    # 比较大小
    best_ = max(best_feature, key=lambda x: x[-1])
    return best_

def train(self, train_data):
    """
    input:数据集D(DataFrame格式)，特征集A，阈值eta
    output:决策树T
    """
    _, y_train, features = train_data.iloc[:, :
                                              -1], train_data.iloc[:,
                                                   -1], train_data.columns[:
                                                                           -1]
    # 1,若D中实例属于同一类Ck，则T为单节点树，并将类Ck作为结点的类标记，返回T
    if len(y_train.value_counts()) == 1:
        return Node(root=True, label=y_train.iloc[0])
    # 2, 若A为空，则T为单节点树，将D中实例树最大的类Ck作为该节点的类标记，返回T
    if len(features) == 0:
        return Node(
            root=True,
            label=y_train.value_counts().sort_values(
                ascending=False).index[0])
    # 3,计算最大信息增益 同5.1,Ag为信息增益最大的特征
    max_feature, max_info_gain = self.info_gain_train(np.array(train_data))
    max_feature_name = features[max_feature]
    # 4,Ag的信息增益小于阈值eta,则置T为单节点树，并将D中是实例数最大的类Ck作为该节点的类标记，返
    if max_info_gain < self.epsilon:
        return Node(
            root=True,
            label=y_train.value_counts().sort_values(
                ascending=False).index[0])
    # 5,构建Ag子集
    node_tree = Node(
        root=False, feature_name=max_feature_name, feature=max_feature)
    feature_list = train_data[max_feature_name].value_counts().index
    for f in feature_list:
        sub_train_df = train_data.loc[train_data[max_feature_name] ==
                                      f].drop([max_feature_name], axis=1)
        # 6, 递归生成树
        sub_tree = self.train(sub_train_df)
        node_tree.add_node(f, sub_tree)
    # pprint.pprint(node_tree.tree)
    return node_tree

def fit(self, train_data):
    self._tree = self.train(train_data)
    return self._tree

def predict(self, X_test):
    return self._tree.predict(X_test)

In[9]：

datasets, labels = create_data()
data_df = pd.DataFrame(datasets, columns=labels)
dt = DTree()
tree = dt.fit(data_df)
In[10]：

tree
Out[10]：

In[11]：

dt.predict(['老年', '否', '否', '一般'])
Out[11]：

In[12]：

data

def create_data():
iris = load_iris()
df = pd.DataFrame(iris.data, columns=iris.feature_names)
df['label'] = iris.target
df.columns = [
'sepal length', 'sepal width', 'petal length', 'petal width', 'label'
]
data = np.array(df.iloc[:100, [0, 1, -1]])
# print(data)
return data[:, :2], data[:, -1]
X, y = create_data()
X_train, X_test, y_train, y_test = train_test_split(X, y, test_size=0.3)
In[13]：

from sklearn.tree import DecisionTreeClassifier
from sklearn.tree import export_graphviz
import graphviz
In[14]：

clf = DecisionTreeClassifier()
clf.fit(X_train, y_train,)
Out[14]：

In[15]：

clf.score(X_test, y_test)
Out[15]：

In[16]：

tree_pic = export_graphviz(clf, out_file="mytree.pdf")
with open('mytree.pdf') as f:
dot_graph = f.read()
In[17]：

graphviz.Source(dot_graph)
Out[17]：

In[18]：

from sklearn.tree import DecisionTreeClassifier
from sklearn import preprocessing
import numpy as np
import pandas as pd
from sklearn import tree
import graphviz
features = ["年龄", "有工作", "有自己的房子", "信贷情况"]
X_train = pd.DataFrame([
["青年", "否", "否", "一般"],
["青年", "否", "否", "好"],
["青年", "是", "否", "好"],
["青年", "是", "是", "一般"],
["青年", "否", "否", "一般"],
["中年", "否", "否", "一般"],
["中年", "否", "否", "好"],
["中年", "是", "是", "好"],
["中年", "否", "是", "非常好"],
["中年", "否", "是", "非常好"],
["老年", "否", "是", "非常好"],
["老年", "否", "是", "好"],
["老年", "是", "否", "好"],
["老年", "是", "否", "非常好"],
["老年", "否", "否", "一般"]
])
y_train = pd.DataFrame(["否", "否", "是", "是", "否",
"否", "否", "是", "是", "是",
"是", "是", "是", "是", "否"])

数据预处理

le_x = preprocessing.LabelEncoder()
le_x.fit(np.unique(X_train))
X_train = X_train.apply(le_x.transform)
le_y = preprocessing.LabelEncoder()
le_y.fit(np.unique(y_train))
y_train = y_train.apply(le_y.transform)

调用sklearn.DT建立训练模型

model_tree = DecisionTreeClassifier()
model_tree.fit(X_train, y_train)

可视化

dot_data = tree.export_graphviz(model_tree, out_file=None,
feature_names=features,
class_names=[str(k) for k in np.unique(y_train)],
filled=True, rounded=True,
special_characters=True)
graph = graphviz.Source(dot_data)
graph
Out[18]：

In[19]：

import numpy as np

class LeastSqRTree:
def init(self, train_X, y, epsilon):
# 训练集特征值
self.x = train_X
# 类别
self.y = y
# 特征总数
self.feature_count = train_X.shape[1]
# 损失阈值
self.epsilon = epsilon
# 回归树
self.tree = None

def _fit(self, x, y, feature_count, epsilon):
    # 选择最优切分点变量j与切分点s
    (j, s, minval, c1, c2) = self._divide(x, y, feature_count)
    # 初始化树
    tree = {"feature": j, "value": x[s, j], "left": None, "right": None}
    if minval < self.epsilon or len(y[np.where(x[:, j] <= x[s, j])]) <= 1:
        tree["left"] = c1
    else:
        tree["left"] = self._fit(x[np.where(x[:, j] <= x[s, j])],
                                 y[np.where(x[:, j] <= x[s, j])],
                                 self.feature_count, self.epsilon)
    if minval < self.epsilon or len(y[np.where(x[:, j] > s)]) <= 1:
        tree["right"] = c2
    else:
        tree["right"] = self._fit(x[np.where(x[:, j] > x[s, j])],
                                  y[np.where(x[:, j] > x[s, j])],
                                  self.feature_count, self.epsilon)
    return tree

def fit(self):
    self.tree = self._fit(self.x, self.y, self.feature_count, self.epsilon)

@staticmethod
def _divide(x, y, feature_count):
    # 初始化损失误差
    cost = np.zeros((feature_count, len(x)))
    # 公式5.21
    for i in range(feature_count):
        for k in range(len(x)):
            # k行i列的特征值
            value = x[k, i]
            y1 = y[np.where(x[:, i] <= value)]
            c1 = np.mean(y1)
            y2 = y[np.where(x[:, i] > value)]
            c2 = np.mean(y2)
            y1[:] = y1[:] - c1
            y2[:] = y2[:] - c2
            cost[i, k] = np.sum(y1 * y1) + np.sum(y2 * y2)
    # 选取最优损失误差点
    cost_index = np.where(cost == np.min(cost))
    # 选取第几个特征值
    j = cost_index[0][0]
    # 选取特征值的切分点
    s = cost_index[1][0]
    # 求两个区域的均值c1,c2
    c1 = np.mean(y[np.where(x[:, j] <= x[s, j])])
    c2 = np.mean(y[np.where(x[:, j] > x[s, j])])
    return j, s, cost[cost_index], c1, c2

In[20]：

train_X = np.array([[1, 2, 3, 4, 5, 6, 7, 8, 9, 10]]).T y = np.array([4.50, 4.75, 4.91, 5.34, 5.80, 7.05, 7.90, 8.23, 8.70, 9.00])
model_tree = LeastSqRTree(train_X, y, .2)
model_tree.fit()
model_tree.tree

Out[20]：